To determine which compound will form [tex]\( CO_2 \)[/tex] and [tex]\( H_2O \)[/tex] when it reacts with an acid, we need to consider the chemical reactions involved for each compound.
Let's analyze the reactions:
1. [tex]\( Mg(OH)_2 \)[/tex] (magnesium hydroxide):
- When [tex]\( Mg(OH)_2 \)[/tex] reacts with an acid (e.g., HCl), the reaction is:
[tex]\[
Mg(OH)_2 + 2HCl \rightarrow MgCl_2 + 2H_2O
\][/tex]
- This reaction produces [tex]\( MgCl_2 \)[/tex] and [tex]\( H_2O \)[/tex], but no [tex]\( CO_2 \)[/tex].
2. [tex]\( NH_3 \)[/tex] (ammonia):
- When [tex]\( NH_3 \)[/tex] reacts with an acid (e.g., HCl), the reaction is:
[tex]\[
NH_3 + HCl \rightarrow NH_4Cl
\][/tex]
- This reaction produces [tex]\( NH_4Cl \)[/tex], but neither [tex]\( H_2O \)[/tex] nor [tex]\( CO_2 \)[/tex].
3. [tex]\( NaC_2H_3O_2 \)[/tex] (sodium acetate):
- When [tex]\( NaC_2H_3O_2 \)[/tex] reacts with an acid (e.g., HCl), the reaction is:
[tex]\[
NaC_2H_3O_2 + HCl \rightarrow NaCl + HC_2H_3O_2
\][/tex]
- This reaction produces sodium chloride ([tex]\( NaCl \)[/tex]) and acetic acid ([tex]\( HC_2H_3O_2 \)[/tex]), but neither [tex]\( H_2O \)[/tex] nor [tex]\( CO_2 \)[/tex].
4. [tex]\( CaCO_3 \)[/tex] (calcium carbonate):
- When [tex]\( CaCO_3 \)[/tex] reacts with an acid (e.g., HCl), it undergoes the following reaction:
[tex]\[
CaCO_3 + 2HCl \rightarrow CaCl_2 + H_2O + CO_2
\][/tex]
- This reaction produces calcium chloride ([tex]\( CaCl_2 \)[/tex]), water ([tex]\( H_2O \)[/tex]), and carbon dioxide ([tex]\( CO_2 \)[/tex]).
Given the reactions above, the only compound that forms both [tex]\( CO_2 \)[/tex] and [tex]\( H_2O \)[/tex] when it reacts with an acid is [tex]\( CaCO_3 \)[/tex].
Therefore, the correct answer is [tex]\( \boxed{4} \)[/tex].
